478 Questions 7 9.7 -7 9.7 0: underground excavation instability mechanisms
Q19.6 For both the haunch A and the side wall B studied in Qs 19.4
and 19.5, and with the information given in Q19.1, calculate the factor of
safety of the block formed by fracture sets 1,2 and 5.
419.7 At a depth of 450 m, a 3 m diameter circular tunnel is driven in
rock having a unit weight of 26 kN/m3 and uniaxial compressive and
tensile strengths of 60.0 MPa and 3.0 MPa, respectively. Will the strength
of the rock on the tunnel boundary be reached if
(a) k = 0.3, and
(b) k = 2.5?
A second tunnel, of 6 m diameter, is subsequently driven parallel to,
and at the same centre line level as, the first such that the centre line
spacing of the two tunnels is 10 m.
Comment on the stability of the tunnels for the field stresses given by
(a) and (b) above.479.8 The diagram shows the relative positions of two parallel hori-
zontal tunnels, each 3 m in diameter. Prior to excavation, the principal
stresses in the area were px = py = pz = 11 MPa.
5m 3m
1-1-1z I
(a) Determine the principal stresses and their directions at point A
after excavation has been completed.
(b) A horizontal fault coincident with the x-axis passes through A. If
the shear strength of the fault is purely frictional with 4 = 20°, will slip
on the fault occur at A?419.9 An ovaloid excavation at a depth of 750 m has in vertical sec-
tion its major axis horizontal, and the ratio of its width to height is 4.
The radius of curvature of its ends is equal to half its height. Assume
that the in situ stress state can be calculated on the basis of complete
lateral restraint in a CHILE medium (ERM 1, Section 4.6.2) with
y = 28.0 kN/m3 and u = 0.3.
An elastic boundary element analysis for k = 0 shows that the stress
in the centre of the roof is -20.5 MPa, and in the side wall is 104 MPa.
An analysis with k = 1 gives corresponding stresses of 4.59 MPa and
84.2 MPa. What stresses would the boundary element analysis give for
the in situ stress state?
Using the equations for stresses in terms of radius of curvature: